 #### Coefficient $B$ for the advanced treatment of the ball-cushion collision time
$B = -2\,b_x^{(i)}\,p_{2y}^{(j)}\,a_y^{(i)}\,p_{2x}^{(j)}+2\,{p_{1x}^{(j)}}^{2}a_y^{(i)}\,b_y^{(i)}+2\,b_x^{(i)}\,p_{2y}^{(j)}\,p_{1x}^{(j)}\,a_y^{(i)}-\\ 4\,a_x^{(i)}\, p_{2y}^{(j)}\,p_{1y}^{(j)}\,b_x^{(i)}+2\,{p_{1y}^{(j)}}^{2}a_z^{(i)}\,b_z^{(i)}-4 \,p_{1x}^{(j)}\,a_y^{(i)}\,b_y^{(i)}\,p_{2x}^{(j)}+2\,a_y^{(i)}\,{p_{2x}^{(j)}}^{ 2}b_y^{(i)}+\\ 2\,a_z^{(i)}\,{p_{2y}^{(j)}}^{2}b_z^{(i)}+2\,{p_{1x}^{(j)}}^{2}a_z^{(i)}\,b_z^{(i)}+2\,a_z^{(i)}\,{p_{2x}^{(j)}}^{2}b_z^{(i)}+2\,b_y^{(i)}\,p_{2x}^{(j)}\,p_{1y}^{(j)}\,a_x^{(i)}-\\ 2\,a_x^{(i)}\,p_{2y}^{(j)}\,b_y^{(i)}\,p_{2x}^{(j)}-2\,p_{1x}^{(j)}\,b_y^{(i)}\,p_{1y}^{(j)}\,a_x^{(i)}-4\,p_{1y}^{(j)}\,a_z^{(i)}\,b_z^{(i)}\,p_{2y}^{(j)}+2\,{p_{1y}^{(j)}}^{2}a_x^{(i)}\,b_x^{(i)}+\\ 2\,a_x^{(i)}\,{p_{2y}^{(j)}}^{2}b_x^{(i)}+2\,a_y^{(i)}\,p_{2x}^{(j)}\,p_{1y}^{(j)}\,b_x^{(i)}-4\,a_z^{(i)}\,p_{2x}^{(j)}\,p_{1x}^{(j)}\,b_z^{(i)}-2\,p_{1x}^{(j)}\,a_y^{(i)} \,p_{1y}^{(j)}\,b_x^{(i)}+\\ 2\,a_x^{(i)}\,p_{2y}^{(j)}\,p_{1x}^{(j)}\,b_y^{(i)} \notag$